Question

How do you differentiate `f(x)=sin(1/(3x-1))` using the chain rule?

Answer 1

`(-3cos(1/(3x-1)))/(3x-1)^2`

Explanation:

differentiate using the`color(blue)" chain rule"`

`d/dx[f(g(x))]=f'(g(x)).g'(x)color(red)" (A)"`
`"-------------------------------------------"`

`f(g(x))=sin(1/(3x-1))rArrf'(g(x))=cos(1/(3x-1))`

and`g(x)=1/(3x-1)=(3x-1)^-1`

`rArrg'(x)=-1(3x-1)^-2 .3=-3(3x-1)^-2=(-3)/(3x-1)^2`
`"-----------------------------------------------------"`
Substitute these values into`color(red)" (A)"`

`f'(x)=cos(1/(3x-1))xx(-3)/(3x-1)^2=(-3cos(1/(3x-1)))/(3x-1)^2`